A057945 - OEIS

%I #16 Mar 10 2019 08:35:50

%S 0,1,2,1,2,3,1,2,3,2,1,2,3,2,3,1,2,3,2,3,4,1,2,3,2,3,4,2,1,2,3,2,3,4,

%T 2,3,1,2,3,2,3,4,2,3,4,1,2,3,2,3,4,2,3,4,3,1,2,3,2,3,4,2,3,4,3,2,1,2,

%U 3,2,3,4,2,3,4,3,2,3,1,2,3,2,3,4,2,3,4,3,2,3,4,1,2,3,2,3,4,2,3,4,3,2,3,4,3

%N Number of triangular numbers needed to represent n with greedy algorithm.

%C a(n) = sum of digits of A000462(n). - _Reinhard Zumkeller_, Mar 27 2011

%C The length of (number of moves in) Simon Norton's game in A006019 starting with an initial heap of n if both players always take, never put. - _R. J. Mathar_, May 13 2016

%H Reinhard Zumkeller, <a href="/A057945/b057945.txt">Table of n, a(n) for n = 0..10000</a>

%F a(0)=0, otherwise a(n)=a(A002262(n))+1.

%e a(35)=3 since 35=28+6+1

%p A057945 := proc(n)

%p     local a,x;

%p     a := 0 ;

%p     x := n ;

%p     while x > 0 do

%p         x := x-A057944(x) ;

%p         a := a+1 ;

%p     end do:

%p     a ;

%p end proc: # _R. J. Mathar_, May 13 2016

%t A057944[n_] := With[{k = Floor[Sqrt[8n+1]]}, Floor[(k-1)/2]* Floor[(k+1)/2]/2];

%t a[n_] := Module[{k = 0, x = n}, While[x>0, x = x - A057944[x]; k++]; k];

%t Table[a[n], {n, 0, 104}] (* _Jean-François Alcover_, Mar 10 2019, after _R. J. Mathar_ *)

%o (Haskell)

%o a057945 n = g n $ reverse $ takeWhile (<= n) $ tail a000217_list where

%o    g 0 _      = 0

%o    g x (t:ts) = g r ts + a where (a,r) = divMod x t

%o -- _Reinhard Zumkeller_, Mar 27 2011

%Y Cf. A000217, A002262, A056944, A057944. See A006893 for records.

%K nonn

%O 0,3

%A _Henry Bottomley_, Oct 05 2000